Cup-type wave gear devices having cup-shaped flexsplines, and “silk hat”-type wave gear devices having “silk hat”-shaped flexsplines are two known types of wave gear device. The basic tooth profile for the circular splines and flexsplines in these wave gear devices is defined by straight lines (Patent Document 1: U.S. Pat. No. 2,906,143), but an involute tooth profile has also been proposed (Patent Document 2: JPB S45-41171). There has also been proposed a method in which the tooth profile of the top lands of both of the splines is determined by a curve obtained by the similarity transformation, performed at a reduction ratio of ½, of the required range for the trajectory along which the teeth of the flexspline move relative to the circular spline, with the trajectory being based on a rack approximation of the teeth of the splines, and the range starting from the critical point of meshing on the trajectory (Patent Document 3: JPA S63-115943).
Here, when the flexspline bent into an elliptical shape by an elliptically-contoured wave generator in the cup-shaped or “silk hat”-shaped wave gear device, is cut in a manner forming a longitudinal section that includes the major axis of the elliptical shape, a bending state is obtained in which the amount of bending gradually increases in a manner nearly proportionate to the distance from the diaphragm side to the open end side (a bending state is obtained in which the amount of bending gradually decreases in a manner nearly proportionate to the distance from the open end side to the diaphragm side). This three-dimensional bending state is referred to as “coning.”
As a result of coning, the tip surfaces of the teeth of one spline end up interfering with the bottom lands of the teeth of the other spline at the open end of the flexspline, and satisfactory meshing cannot be obtained in a case in which the tooth profiles of the two splines are designed so that the teeth have the same depth in the tooth trace direction, as is the case with the teeth employed in typical flat gears.
It has previously been proposed that end relief machining be carried out on the top parts and bottom parts of the external teeth of the flexspline at the open end side thereof so as to cause the teeth to gradually recede in the direction from the circular spline in order to prevent the coning-induced tooth interference. Such a modification of the tooth profile is disclosed, for example, in Patent Document 4 (WO96/19683, FIG. 11) and Patent Document 5 (Japanese Utility Model Registration No. 2535503, FIG. 11).
However, linear machining such as that used for a typical flat gear cannot be used to perform gear cutting on a flexspline having such a modified tooth profile, and a problem is therefore presented in that limitations are imposed on the gear cutting methods that can be used.